Pulse code modulation (PCM) signals consist, in general, of a series of binary code words wherein each word represents an instantaneous value of a periodically sampled and quantized analog signal. In normal usage these code words are transmitted in the form of a serial bit stream to a receiving station where they are decoded into a reconstructed version of the original analog signal. In between, the processing of the digital signal usually involves various operations being performed on the PCM words. For example, the present inventor in "A Twelve-Channel Digital Echo Canceler", IEEE Transactions on Communications, Vol. COM-26, No. 5 (May 1978), pp. 647-653 discloses an echo canceller employing floating point multipliers. However, the typical PCM word is not in a floating point representation. Hence, a converting operation need be performed to convert the PCM code word into a floating point representation thereof. A floating point representation of a number z is a representation of the form EQU z=S.multidot.A.multidot.B.sup..varies. ( 1)
where S is the polarity, or sign, of the number; A is its mantissa; B is its base, which generally equals two in a binary system; and .varies. is its exponent.
Where the PCM code is linear, i.e., having no compression or expansion, a simple shifting of the binary digits can produce a multiplication or division in powers of two. A linear code is therefore readily adapted to a floating point representation. On the other hand, where the PCM code is nonlinear, e.g., a compressed code, a simple shift does not produce a uniform multiplication or division. The telecommunications art usually employs a nonlinear PCM code.
In a special issue on digital signal processing, an article by A. Kundig, "Digital Filtering in PCM Telephone Systems", IEEE Transactions on Audio and Electroacoustics, Vol. AU-18, No. 4 (December 1970), pp. 412-417 discloses a method for converting a nonlinear PCM word, encoding according to the so-called A-law, into a floating point number representation. The Kundig method succeeds, in part, because of the close relationship between A-law encodings and floating point encodings.
A second nonlinear PCM code, known as the .mu.-law, approximates the compression function: ##EQU1## Known .mu.-law to floating point converter arrangements are of two types. One type includes a memory which, responsive to the PCM word, has extended from a location therein the floating point representation. For a common 8-bit PCM word having one sign bit such arrangements typically employ a memory having at least 2.sup.7 locations, each location with an eight bit floating point representation. The second type is a two stage converter including a .mu.-law to fixed point conversion followed by a fixed point to floating point conversion. Hence, known .mu.-law to floating point converters tend to be expensive.